Resolution-dependent Eddy Parameterizations for Large-scale Ocean Models

Transcription

1 Resolution-dependent Eddy Parameterizations for Large-scale Ocean Models Robert Hallberg with contributions from Alistair Adcroft NOAA / GFDL and Princeton University

2 Mercator/Tripolar Resolution Required to Admit st Baroclinic Deformation Radius Coupled Climate Model: ~5 years/day on ~0,000 Processors requires ~/4 res.

3 u t h t h t Phillips model of baroclinic instability -layer stacked shallow water model. (See textbook discussion in Pedlosky, 987.) f kˆ u u M u T cd u k u M g / g x M M 3/ h u K 3/ 3/,Ref h 3/ x h u K 3/ 3/,Ref h 3/ Exhibits instabilities with peak growth rates at wavelengths of p def. Restoring of zonal-mean interface height reenergizes the flow. Strong bottom drag prevents barotropization. (Arbic & Flierl, 006) 0 h, u / 3/ h 3/ D h 0 km h, u 40 km Def f gh h h h

4 Upper Layer Lower Layer 0 km Resolution, K h = 0 Day Day 0 Day 35 Day 730

5 Upper Layer Flow at Various Resolutions, Day 730, K h = 0.5 km 5 km 0 km 0 km 5 km 33 km 40 km 50 km

6 Upper Layer Relative Vorticity / Coriolis at Various Resolutions, Day 730, K h = 0.5 km 5 km 0 km 0 km 5 km 33 km 40 km 50 km

7 Effects of Resolution on Eddy-Driven Overturning Average Years - 0 Def f gh h h h 5 35km Baroclinic eddy effects are absent or need to be parameterized when the deformation radius is poorly resolved.

8 Relative Vorticity Upper Layer Flow Effects of Interface Height Diffusion (G-M mixing) at 0 km Resolution, Day 730 K h =0 m s - K h =000 m s - K h =3000 m s -

9 Overturning Transport (0 6 m 3 s - ) Interface height diffusion is much more effective at suppressing eddies than at parameterizing their effects! Interface Height Diffusivity (m s - ) Interface Height Diffusivity (m s - )

10 One Proposed Solution: Scale Laplacian horizontal viscosities and diffusivities by a function of the ratio of the grid spacing to the deformation radius: K K F 0 Def ~ / A reasonable choice might be F Def R R 4 f c g c g ~ R Def ~ / x y Has been used for a few years in GFDL s ESMG & eddy-rich ocean models. For the Phillips model, this fails there is a transport gap where the eddies are partially parameterized but efficiently suppressed. R Def ~ /

11 Total Overturning at Various Resolutions, F(R) = /(+R 4 ) Parameterized vs. Explicit Eddy Transports, 0 km Res. Time- & Zonal-mean Diffusivity K K / 4 0 ~ Def

12 The best solution for the Phillips problem: Abruptly disable the Laplacian interface height diffusivity once the ratio of the grid spacing to the deformation radius reaches a value >: ~ K0 Def / R K ~ 0 Def / R Trans Trans Def f c g c g ~ x y This works reasonably for the Phillips problem for any R trans >~! K/K 0 R Def ~ /

13 Total Overturning at Various Resolutions, Step Function Parameterized vs. Explicit Eddy Transports, 0 km Res. Time- & Zonal-mean Diffusivity ~ K0 Def / K ~ 0 Def / R R Trans Trans

14 Total Overturning at Various Resolutions, F(R) = /(+R 4 ) Parameterized vs. Explicit Eddy Transports, 0 km Res. Time- & Zonal-mean Diffusivity K K / 4 0 ~ Def

15 The total fluxes match smoothly, even with a step-function change in diffusivity Resolved eddies Parameterized eddies

16 Varying Values of the Transition Relative Resolution R Trans RTrans R Trans 3 4 RTrans R Trans 3 40 km 33 km 0 km 6 km 0 km Underresolved eddies at transition Well resolved eddies at transition

17 /(+R 4 ) Diffusivity Scaling in a Global Model / 8

18 MEKE and Resolution Scaling The resolution scaling seems particularly promising when combined with a parameterize to diagnose the unresolved Mesoscale Eddy Kinetic Energy (Marshall & Adcroft, 00; Eden et al., 008): E t Src Int c Src E d u H bot E H H E K K? 0.00? g k Int k H F k R MEKE Background H E k 0.3? min, x y E MEKE D h k u k Visc E : Unresolved Mesoscale Energy/Mass in Column MEKE is self-regulating; the mixing changes the resolved state to eliminate its source.

19 MEKE in Global Models with F(R)=/(+R 4 ) / 8

20 The Gulf Stream in Global Models with Resolution Scaling and MEKE / 8 With MEKE and Resolution Scaling, these global ocean models differ only in their choice of grid-spacing and time-step.

21 Summary No global ocean model resolves eddies everywhere. Eddies should be parameterized where they are not resolved. Parameterizations of eddy effects are imperfect; it is better to represent eddies explicitly where they are adequately resolved. Popular eddy parameterizations are better at suppressing eddies than they are at mimicking them. Solution in Phillips Model: Abruptly disable eddy parameterizations where the dominant eddy scales ( st baroclinic deformation radius) are well resolved.